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A114775
Expansion of x^2*(1+x^2)*(1 - x^4 + x^7)/((1 - x^4 + x^6)*(1 - x^4 - x^6)).
1
0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 4, 3, 4, 5, 7, 5, 7, 9, 12, 9, 12, 16, 21, 16, 21, 28, 37, 28, 37, 49, 65, 49, 65, 86, 114, 86, 114, 151, 200, 151, 200, 265, 351, 265, 351, 465, 616, 465, 616, 816, 1081, 816, 1081, 1432, 1897, 1432, 1897, 2513
OFFSET
0,14
FORMULA
Let M = {{0, 1, 0}, {0, 0, 1}, {-I, -1, 0}}, v(0) = {0, 1, 1}, and v(n) = M*v(n-1) then {a(n), a(n+1)} = {abs(Re( v(n)((1)) )), abs(Im( v(n)((1)) ))}.
G.f.: x^2*(1+x^2)*(1 - x^4 + x^7)/((1 - x^4 + x^6)*(1 - x^4 - x^6)). - Colin Barker, Jan 01 2013
MATHEMATICA
M = {{0, 1, 0}, {0, 0, 1}, {-I, -1, 0}}; v[0] = {0, 1, 1};
v[n_]:= v[n] = M.v[n-1];
Flatten[Table[{Abs[Re[v[n][[1]]]], Abs[Im[v[n][[1]]]]}, {n, 0, 40}]]
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 82);
[0, 0] cat Coefficients(R!( x^2*(1+x^2)*(1-x^4+x^7)/(1-2*x^4+x^8-x^12) )); // G. C. Greubel, Jul 08 2021
(Sage)
def A114775_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( x^2*(1+x^2)*(1-x^4+x^7)/(1-2*x^4+x^8-x^12) ).list()
A114775_list(82) # G. C. Greubel, Jul 08 2021
CROSSREFS
Cf. A000931.
Sequence in context: A265626 A230230 A187821 * A071136 A025425 A234451
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Feb 21 2006
EXTENSIONS
New name from Colin Barker, Jan 01 2013
Edited by G. C. Greubel, Jul 08 2021
STATUS
approved